Physics 130
Final Examination - Wave Motion, Optics, and Sound
December 15th, 2012, 2:00 pm 5:00 pm Pavilion
All Sections (Consolidated)
Course Convener: John P. Davis
NAME:
ID #
A single 8 1/2 x 11 formula sheet (front and back) is permitted.
Calculators

University of Alberta
Department of Mathematical & Statistical Sciences
Math 100 Fall 2016
Section
EA1
Instructor
V. Yaskin
Office
CAB 583
EB1
E. K. Leonard
CAB 679
EC1
G. Tokarsky
CAB 469
ED1
V. Troitsky
CAB 511
EE1
V. Yaskin
CAB 583
EG1
S. Graves
CAB 52

Optimization Problems Solutions
1.
Constraint: y=12x2
Maximize: A=2 xy
It follows that A=2 x 12x 2 =24 x2 x 3 .
x
y
and hence
y
x
dA
2
=246 x .
dx
The critical points are x=2 .
Plugging this into the constraint yields y=8 .
he maximum area is A=32 units2.

lim sin x =0
x 0
lim
x 0
lim cos x =0
x0
x
=1
sin x
lim
x 0
lim
x 0
cos x 1
=0
x
sin x
=1
x
1cos x
lim
=0
x
x0
Trig Identities
sin2 x cos 2 x=1 sec 2 x =1tan2 x
csc 2 x =1cot 2 x sin2x =2sin x cos x
2
2
cos 2x=cos x sin x
=2cos2 x 1
=12sin2 x
sin( x +

Slant Asymptotes
If the graph of a function f (x) approaches a particular line y=mx + b as x goes to infinity and/or
negative infinity, then we say that f (x) has a slant asymptote.
In rational functions, slant asymptotes occur when the degree of the nume

University of Alberta
Department of Mathematical & Statistical Sciences
MATH 101(EQ1)-WINTER 2017
CALCULUS II
Instructor: Dragos Hrimiuc
Office: CAB 585
Email: [email protected]; Phone: 780- 492-3532
Office Hours: 11:0011:50 (MW), 9:00-9:50(F)
Lecture

MATH 101-MIDTERM EXAM
Winter Term 2017
SATURDAY, March 4
Time: 13:00-14:30
EXAM PROTOCOL
Photo ID (One Card) will be required to write the exam. Please place it on the top of the desk.
No books, notes, calculators or other electronic aids are allowed!
The

Section D1
Dr. Mustafa Gl
Week 9: Shear force and bending moment (equations and diagrams)
Relationships between distributed load, shear force, & bending moment
Fall 2016
Shear and Moment Eqns & Diagrams
Thus far we have looked at the calculation of intern

EXAMPLE 1: A 3-PIN ARCH
Solve for the reactions at the pins of the threepin arch shown below.
10 kN
WW T w
2000
1500
Cx
3 timtm L; WW g; 24%;? I QQEH 0?
>5? MCT g5; Wijizf fggffiiif To develop additional equations, we must break

Section D1
Dr. Mustafa Gl
Week 8: Frames and machines;
Internal forces in members
Fall 2016
Frames & Machines
2
Frames & Machines
3
What is a Frame?
Trusses:
Consist of 2-force members which are loaded only at
the joints.
Frames:
Consist of members which

Partial Derivatives
Given a function f with more than one independent variable, we can take the partial derivative of the
function with respect to one of the variables. That is, if f is a function of the n variables x1 , x 2 , , x n ,
f
then the partial d

Programs and pseudo code algorithms
The concept of a program
A computer program is a sequence of instructions or programming language statements that a
programmer must write to make a computer perform certain tasks. Programmers need some
knowledge on pro

Standing Waves
cf s
o =
vs
Lens eqn:
=observed wavelength and
c o=c+ v o and
Magnification:
c vo
f o=
.f
c v s s (toward or away)=observed frequency
(
)
Opening angle of shockwave
Node-to-node distance =
sin =
ct
vs t
thus
=sin1 (
2 and AN-to-N distance =

Name: Solutions
Math 53: Quiz 2
September 9, 2014
1. (1 point) Find the Cartesian equation of the curve and sketch it: x = cos() , y =
1 + sin(), 0 < 2.
We have cos() = x and sin() = y 1. Thus,
cos2 () + sin2 () = 1 x2 + (y 1)2 = 1.
This represents a circ

Chapter 5 Integrals
5.1 Calculating Areas using Riemann Sums
We have nice formulas for calculating the area of a circle, rectangle, parallelogram, triangle, etc.
What about the area under the curve f x=x 2 , above the x-axis and between x=0 and x=5 ?
We c

Formula
Sheet
MATH 101
Basic Integrals:
Z
Z
tan(x)dx = ln | sec(x) | +C
Z
cot(x)dx = ln | sin(x) | +C
Z
sec(x)dx = ln | sec(x)+tan(x) | +C
csc(x)dx = ln | csc(x)cot(x) | +C
Z
Z
1
1
x
x
1
dx = arctan( ) + C
dx = ln | x2 + a2 | +C
x2 + a2
a
a
x2 + a2
2
Z
x

SPH4U: Unit Test Dynamics
Name _
Part B: Theoretical Question (4 marks)
Answer the following questions in the space provided. Be sure to provide a well thought out answer for each question;
provide mathematical support when applicable.
1) The diagram belo

SAMPLE TEST - Energy, Work, SHM, and Momentum
Short Answer
Answer the following questions on the paper provided. Marks indicated are meant to act
as a guide and may not be the actual value when evaluated.
1. Consider two linear pendulums set in motion. Sp

PHYS 130
Course Outline
UNIVERSITY OF
Autumn 2016
DE PA RTM E N T OF
ALBERTA PHYSICS
PHYS 130 Waves and Optics
Section EA02
Instructor
Dr. Roger Moore
Office
CCIS 2-083
Office Hours
Wed 12:00-14:00 and Thu 13:00-15:00. I also operate an open door policy y

Example 5: Internal Forces
. Determine the internal normal force, shear force, and bending moment
at points C and D in the beam.
60 lb/ft 690 lb
[j : [:('(5'+) (~20 (g/H) : (30 (1;
IUSPH HO I/Pf) 6a; ('6 F ' oi
215:0 = AX (7o) ~> M5251; ~> (
Z M)4 : O r

NM 2] 10/0
Example 3: Machine Equilibrium
The scale (a type of machine) consists of five pin-connected members.
Determine the load W on the pan EG if a weight of 3 Ibis suspended
from the hook at A.
CD FBDs. 5,. 3. 2 CE M1 DF
3H, 13 C/ 9 M; ' (X:0
/ Q20

Name: Maggie Wu
Date: 2016/05/08
Class: SPH4U Period2
Catapult Report
Introduction: A catapult was made to launch a marshmallow at a target on the floor. Some
measurements of the catapult were done to determine the launch velocity of the
marshmallow and t

Names: Iswara Nagulendran and Hashir Memon
Date: May 11, 2015
Teacher: Mr. Blanchard
Course Code: SPH4U
Analysis of Catapult Report
Measurements:
The following are the measurements were taken from the catapult:
Mass of Throwing Arm:
Length of Throwing Arm

Analysis of Catapult
Report
BY: JIA
HAO XU
Course: SPH4U1
Teacher: Ms. Nasreen
Date: November 20 , 2015
th
Diagram of Catapult:
Variables Defined:
rm
Distance between pivot and marshmallow
rc
Distance between pivot and center of mass
hm 2
Height of marshm

Name: Maggie Wu
Date: 2016/05/08
Class: SPH4U Period2
Catapult Report
Introduction: A catapult was made to launch a marshmallow at a target on the floor. Some measurements
of the catapult were done to determine the launch velocity of the marshmallow and t

Name: Maggie Wu
Date: 2016/05/01
Class: SPH4U Period2
Strength of a Magnetic Field in a Coil Lab
Abstract: A current balance was inserted into a helix and each of them was connected to a power
supplies. The predicted magnetic field found by theory and the

Written Assignment 3
Math 100 Fall 2016
Due: Friday, November 18 at 11 pm
Total: 100 points
Please complete each problem on a separate piece of paper. You will need to scan your work
and submit it electronically through Crowdmark. The link will be sent to

Written Assignment 2
Math 100 Fall 2016
Due: Friday, October 21 at 11 pm
Total: 100 points
Please complete each problem on a separate piece of paper. You will need to scan your work
and submit it electronically through Crowdmark. The link will be sent to

Written Assignment 4
Math 100 Fall 2016
Due: Wednesday, December 7 at 11 pm
Total: 100 points
Please complete each problem on a separate piece of paper. You will need to scan your work
and submit it electronically through Crowdmark. The link will be sent